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Scalar and Vector Operations

Problems involving scalar and vector operations

The eastward component of vector A is equal to the westward component of vector B and their northward components are equal. Which one of the following statements is correct for these two vectors? Choices: Vector A is parallel to vector B Vector A is anti-parallel to vector B The magnitude of vector A is equal to the mag

Direction relative to ground

A plane has an airspeed of 142 m/s. A 30 m/s wind is blowing southward at the same time as the plane is flying. What must be the direction of the plane in order to move due east relative to the ground? Answer choices: 78.1 degrees north of east 11.9 degrees north of east 77.8 degrees north of east 12.2 degrees north of

Vector A=6 m and points 30 degrees south of east. Vector B=4 m and points 30 degrees south of west. Find the resultant vector A+B. Answer Choices: 3.3 m at an angle of 71 degrees south of east. 5.3 m at an angle of 71 degrees south of east 3.3 m at an angle of 19 degrees south of east 5.3 m at an angle of 19 degrees sou

Velocity of a charge moving in a magnetic field

The problem states: A particle with a charge of -5.90 * 10^-9 C is moving in a uniform magnetic field B(vector) = -(1.25 T) k (hat). The magnetic force on the particle is measured to be F(vector) = -(4.00 * 10^-7 N) i(hat) + (7.60 * 10^-7 N) j(hat). 1. Are there components of the velocity that are not determined by the

Vector problem

So here is the question Let A= {10, 30°} be a vector of magnitude 10 ( in some units) and pointing in a direction of 30°counter-clockwise from positive x. Let B = { 7, 225°degree} Find x and Y componens of these two vectors A { AX= AY= B { Bx= BY= Find x and y components of the sum S= A+B S= { Sx= S

Resultant Vectors of 3 Displacement Vectors

How do I find the resultant of the three displacement vectors in the drawing by means of the component method? If the magnitudes of the vectors are A= 5 m B=5 m and C= 4 m?

Magnitude and Direction of a Resultant Vector

If Displacement vector A points due east and has a magnitude of 2.00 km. Displacement vector B points due north and has a magnitude of 3.75 km. Displacement vector C points due west and has a magnitude of 2.50 km. Displacement vector D points due south and has a magnitude of 3.00 km. How can I find the magnitude and direction (

Pair of forces

Consider a pair of forces, one having a magnitude of 20 N, and the other having a magnitude of 12 N. What maximum net force is possible for these two forces? What is the minimum net force possible?

electric field and potential of point like charges.

(See attached file for full problem description) --- Two equal, positive charges, q = 2.0 micro Coulomb ; are located on the x-axis- one at +0.3m and the other at -0.3m. A third charge Q = +4.0 micro Coulomb is located on the y-axis at +0.4m 1) Find the magnitude & direction of the resultant (net) force on Q. 2) Find

Stokes and Gauss' Theorem

1. A vector ﬁeld v(x, y, z) is given by the formula v(x, y, z) = xyˆx − yˆ2y. Consider a square path in the xy plane which starts at (0,0,0) and moves along the corners (1,0,0), (1,1,0) and (0,1,0). Calculate the path integral of v, i.e. v · dr, and calculate the area integral of the divergence, R ∇ × v · da, an

Center of Mass of Particles

A) Find the xcm coordinate of the center of mass of the system of particles shown in the figure. (See attached file for full problem description with diagram and values) Express your answer in meters to two significant figures. xcm = B) A straight rod has one end at the origin and the other end at the point (L,0) and

Center of Mass and Coordinate System

A system of four buckets forms a square as shown in the figure. Initially, the buckets have different masses (it is not known how these masses are related). A student begins to add water gradually to the bucket located at the origin. As a result, what happens to the coordinates of the center of mass of the system of buckets? (Se

Find the x coordinate of the center of mass.

Please see the attached file for full problem description with diagram. For the system of particles described above, find the x coordinate xcm of the center of mass. Assume that the particle of mass M is at the origin and the positive x axis is directed to the right. Express your answer in terms of L.

Finding the force on a helicopter given its position vector as a function of time.

(See attached file for full problem description with proper symbols) The position of a 2.75 x 10^5 N training helicopter under test is given by Vector r = (0.020 m/s3)t3î + (2.2m/s)t&#309; - (0.060 m/s2)t2k Find the net force on the helicopter at t =5.0 s. Express the vector F in the form Fx, Fy , Fz , where th

Direction and Work Done by Electric Field

(See attached file for full problem description) --- 4 a) Sketch arrows on the diagram (see attachment) to indicate the direction of the electric field, if any, at each of the points A, B, C, and D. A positively charged test particle is observed to move as described below. For each motion, tell whether the work done by

Vector calculation of a plane

A plane leaves the airport in Galisto and flies a distance 170 km at an angle 68.0 degree east of north and then changes direction to fly a distance 270 km at an angle 48.0 degree south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, how far should this crew

8 Problems Vectors: Components of a vector, resultant vector

(See attached file for full problem description with diagrams) --- Please solve each and give a complete detailed step by step solution to solving each problem no matter how easy. I am trying to learn and not an expert. Give answer and way to solve. Adult student trying to make my way through all this and need your help!

Force Impulse and Projectile Motion

In a slow-pitch softball game, a 0.200 kg softball crossed the plate at 20.00 m/s at an angle of 35.0° below the horizontal. The batter hits the ball toward center field, giving it a velocity of 40.0 m/s at 30.0° above the horizontal. (a) Determine the impulse delivered to the ball. (b) If the force on the ball increase

Body on slope with friction

Please help with the following problem. Provide step by step calculations for each problem. You have a mass of 59 kg and are on a 28-degree slope hanging on to a cord with a breaking strength of 224 newtons. What must be the coefficient of static friction to 2 decimal places between you and the surface for you to be saved fr

Kinematics and Energy Kinematics

Could you provide workings out and answers to the following physics questions: 1.a. What is the difference between a scalar and a vector quantity? b. A hiker walks due north for 4.0 km to reach point A and then northeast for 6.0 km to reach point B. Find by calculation or by scale drawing: - the straight line distance from s

Physical principles; difference between a vector and scalar distance, difference between speed and velocity

1. Understanding physical principles is often very useful in everyday life. For example, a skater develops an intuitive understanding of angular momentum in order to master making turns, and virtually all of us as car drivers come to understand the principles of inertia, velocity, and linear momentum. Can you name at least

Calculations for Vectors

Please provide formulas and step by step instructions on how to solve. A Vector F has a magnitude of 20 and is directed vertically downward. Find is components Fx and Fy in each of the coordinate frames. Please see attached.

Solving Vector Problems

Hi, I am having a lot of difficulty understanding vectors, can you please assist me with these questions. Given: position vector A = i hat. position vector B = i hat + j hat + k hat. 1) Find A hat and B hat (unit vector in that direction). 2) Find position vector C in that plane perpendicular to position ve

MAGNITUDE OF A VECTOR

If A=(12i-16j) and B=(-24i+10j),what is the magnitude of vector C=(2A-B)?

Extremal paths.

Consider the action for a particle in a potential U. a. Show that an extremal path is never that of a local maximum for the action. ("Local" means relative to nearby paths). b. Find an example in which an extremal path is that of a local minimum for the action. c. Find an example in which an extremal path is not that of a

Vectors Magnitudes and Angles

1) Both vectors A and B have a magnitude 5 and the angle between them is 53.13 degrees. Calculate the magnitude of A+B. 2) The diagram shows vector C. Determine the X and Y components of C. see attached file for details

Evaluating quantities of vectors

Two vectors are given by A = -3i + 7j -4k and B = 6i -10j + 9k. Evaluate the quantities: a) cos^-1 [A.B/AB] ( the . between the A.B is a dot product) b) sin^-1 [ |A x B|/AB] c) Which gives the angle between the vectors. I haven't a clue as to what to do with this problem. Do I use the cross products of unit vectors t

Vector Additions - Analytically and Graphically

See the attached file. Finding the vector sum of three forces 1) Experimental method: Use F1 of 160g at 280 degrees, F2 of 105 grams at 60 degrees and F3 of 75g at 15 degrees counter clockwise from the +y axis. Determine the equilibriant and the resultant of the three vectors experimentally. Record magnitude and direction

Calculating magnitude of a vector and height

If A = (12i - 16j) and B = (-24i+10j), what is the magnitude of the vector C=(2A-B)? Answers: a) 42 b) 22 c) 64 d) 90 An archer shoots an arrow with a velocity of 45 m/s at an angle of 50 degrees with the horizontal. What is the height of the arrow at a point 150 meters downrange? Answers: a) 4.7 m b) 47.0 m c) 5

Angle between two vectors

The vector A has a magnitude of 6m and vector B has magnitude of 4 m. That is the angle between them if the magnitude of the resultant is (a) 3m (b) 8m? Let vector A lie along the x-axis. Do each part graphically and by components.